How to Read and Do Proofs: An Introduction to Mathematical Thought Processes, 5th Edition

How to Read and Do Proofs has been teaching students how to do
proofs for over 20 years!

This text provides a systematic approach for teaching
undergraduate and graduate students how to read, understand, think
about, and do proofs. The approach is to catagorize, identify, and
explain (at the student's level) the various techniques that are
used repeatedly in all proofs, regardless of the subject in which
the proofs arise. How to Read and Do Proofs also explains
when each technique is likely to be used, based on certain key
words that appear in the problem under consideration. Doing so
enables students to choose a technique consciously, based on the
form of the problem. Students are taught how to read proofs that
arise in textbooks and other mathematical literature by
understanding which techniques are used and how they are applied.
It shows how any proof can be understood as a sequence of the
individual techniques. The goal is to enable students to
learn advanced mathematics on their own. This book is suitable as:
(1) a text for a transition-to-advanced-math course, (2) a
supplement to any course involving proofs, and (3) self-guided
teaching.

The inclusion in practically every chapter of new material on how to read and understand proofs as they are typically presented in class lectures, textbooks, and other mathematical literature. The goal is to provide sufficient examples (and exercises) to give students the ability to learn mathematics on their own.

The Instructor's Solutions Manual contains the solutions to all of the exercises and is available as a download from the websiteon the Instructor Book Companion Site. Not only short answers, these solutions are often given in detail, with a full explanation of the thinking process that goes into the solution.